Here, I just made one for you, based on information available from the actual game files.
Click the image to see a larger version!
This is updated up to the June 2011 patch and DLCs; however, unique units always upgrade in exactly the same way as the units they replace, so if some unique unit is missing from the chart above you can just find out what it replaces to see how it upgrades.
Gun units and melee units are not the same - in particular, they differ in some promotions, you can check my promotion chart which uses the same icons.
The Giant Death Robot is indeed considered an armor unit.
Missiles, bombs and SS parts are non-upgradable (and removed from the chart for brevity).
The Civilization 5 manual does not have such a chart, and neither is there one in the game like the tech tree. (I do not know if the physical copy of the game comes with any charts.)
However, you can use the Civilpedia to build one. Look up whichever unit you are concerned about. The Civilpedia will show what it upgrades to, which you can click on to get to that unit, and follow that unit in turn.
Units can usually upgrade within their type: Melee to Melee, Range to Ranged, Mounted to Mounted, Siege to Siege... Except that Melee and Ranged eventually upgrade to the same Gunpowder track.
Melee is split into (at least?) two upgrade paths: one for the anti-mounted Spearmen->Pikemen, and the other for the general units.